Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes. (English) Zbl 0936.60037

Wu, Liming

Ann. Inst. Henri Poincaré, Probab. Stat. 35, No. 2, 121-141 (1999).

The author extends forward-backward martingale decomposition of Meyer-Zheng-Lyons’s type from the symmetric case to the general stationary situation for the partial sum \(S.(f)\) with \(f\) satisfying a finite energy condition. Furthermore, as corollaries, he obtains a maximal inequality and a tightness result related to the functional central limit and a criterion of a.s. compactness related to the functional law of iterated logarithm.

Reviewer: Zdzislaw Rychlik (Lublin)

MSC:

60F17	Functional limit theorems; invariance principles
60J55	Local time and additive functionals

Keywords:

forward-backard martingale decomposition; Donsker’s invariance principle; Strassen’s strong invariance principle